TRUSS BRIDGE ANALYSIS - TRUCK WEIGHTS

SUBMITTED BY:

HAZIM AL KHUSAIBI

DEPARTMENT OF CIVIL AND ENVIRONMENTAL ENGINEERING

PENNSYLVANIA STATE UNIVERSITY

EMCH 461 FINAL PROJECT SUBMITTED TO DR. I. SMID

F I N I T E E L E M E N T A N A L Y S I S

Engineering Mechanics 461

•

H a z i m A l K h u s a i b i • E m a i l ; H s a 5 0 0 6 @ p s u . e d u

Table of Contents

Background! 1

Finite Element Analysis! 1

Truss Bridge! 1

Introduction! 2

General Introduction to Project! 2

Geometry! 2

Approach & Formulation! 4

Assumptions! 4

Program Selection & Other ANSYS Assumptions! 5

Problem Formulation ! 5

Analysis! 6

Part 1: Control Analysis:! 6

Part 2: Analysis After 75 year Cycle:! 7

Results! 8

Reaction Forces:! 8

Deflection:! 9

Axial Stress:! 9

Discussion:! 10

Conclusion! 10

Results & Improvements to Model:! 10

Finite Element Methods Discussion:! 11

Appendix ! 12

List of Figures! 12

List of Tables! 12

Glossary! 13

Bibliography & Programs Used! 14

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Background

Finite Element Analysis

Finite Element Method can be defined as the numerical method for solving problems of engineering

and mathematical physics. Fields usually frequented by the finite element method range from

structural analysis, mass transport, fluid flow and heat transfer. For complex cases and geometries it is

also possible to obtain an analytical mathematical solution but this will not be emphasised much on

this project. Developed in the 1940s by Structural engineers (Hrennikoff & McHenry) the finite element

method increasingly evolved with the aid of computer programming, from being a lattice of single

dimensional analysis to an enormous and advantageous application in solving complicated

engineering programs from structural engineering to bioengineering.1

Truss Bridge

Truss structures are composed of members that are connected to form a rigid frame of steel, this broad

application can be used in many areas, such as roof structures rail road and other transportation

bridges. The individual members of a Truss Bridge are the load carrying components of the structure,

they are arranged in a triangular manner resulting in the loads carried to become either in tension or

compression. Today bridge trusses are mainly used for short span distances, since suspension and

other advanced bridges with modern concrete & steel standards. ! !

!

! Typical Short Span Truss Bridge

! used in project

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1 Logan, Daryl L. A First Course in the Finite Element Method. Detroit: Cengage-Engineering, 2006. Print.

Figure 1

Introduction

General Introduction to Project

As a senior in the Civil Engineering program with an emphasis in Structural Engineering, Bridges play

an important role in the fundamentals of Structural Design. Especially since bridges undergo a variety

of loads, such as wind, snow and the transient loads due to the vehicular traffic utilising the bridge.

Today, in the United States alone, thousands of aged bridges are in active service, challenging many

municipalities and state governments to spend millions and hire many engineers to evaluate the

structural integrity of the bridge. Avoiding disasters such as the collapse of the I-35 W Mississippi River

Truss-Arch Bridge in Minnesota. (Date of Incident: Wednesday, August, 1st 2007)

My project’s aim is to highlight the affect of vehicular transient loads, mainly the loads due to heavy

duty trucks utilising a short span truss bridge, by emphasising the results of deflection due to loads of a

Truss Bridge before and after ageing 75 years. The properties I found very important to consider after

this time are: Fatigue, accumulation of rust, cross bracing distortion and the reduction of redundancy at

the connection points of the girders.

Geometry

The bridge chosen for this project, is a Howe Truss Configuration bridge, consisting of cross braced

deck truss and a multi steel girder spans. The bridge geometric properties are as follows:

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1 Short spanned bridge that is 40 m (~130 ft) long

2 Base Girders that are 5 m each (W21x44)

3 Diagonal truss beam are 9.43 m each (W14x22)

4 The hight of the Truss Girder is 8 mTable 1

The geometry combined results in the following arrangement in the finite element analysis software,

ANSYS. The base girders and beams are all connected via gusset plates and are cross braced on the top

as well as the bottom where the pavement sits, the bridge carries a two way, four-lane road that serves

about 7,500 trucks per day.

This table to the right illustrates how the key-

points are assigned to the coordinate system

(x,y) in ANSYS forming the truss shown in

the image above. Please refer to the text input

attached to the Glossary section for more

information and the (.txt) file used to execute the command.

The following material properties and element type were used to model the truss bridge configuration

into ANSYS.

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1 2 3 4 5 6 7 8

0, 0 5, 0 10, 0 15, 0 20, 0 25, 0 30, 0 35, 0

9 10 11 12 13 14 15 16

40, 0 35, 8 40, 8 25, 8 20, 8 15, 8 10, 8 5, 8

Table 2

Figure 2: ANSYS model showing member and nodal assignment

ELEMENT USED TO REPRESENT (GIRDERS & BEAMS)

POISSON’S RATIO

MODULUS OF ELASTICITY

LINK 1

0.29

200 GPa

Approach & Formulation

Assumptions

To make this FEA problem much simpler, several basic assumptions have been made. The assumptions

made concern the properties of the steel girders, the type of connections of the steel girders and beams,

the amount of live load due to the transient load and finally the location of the load between the two

cases.

1. Girder - Beam Connections: The girder-beam connections used in an actual Truss Bridge uses gusset

plates, for simplification, the gusset plates were omitted from the finite element analysis and instead,

simply line connections converging to a point were used instead. As illustrated below.

2. Beam-Girder Cross Sectional Area: The average cross-sectional area is assumed as (3250 mm2).

3. The (ADT): The Average Daily Traffic will be assumed as 15,000 trucks in both directions, as the

bridge is mainly a cargo route.

4. Predicted Average Life: The predicted average life at a typical live-load stress of 138 MPa, is between

20,000 and 40,000 cycles.

5. Lane Loading: The Lane loading is set using the maximum AASHTO legal limit of 356 kN, at a

spacing of 38 m. A single point load of 356 kN will be used at the mid point of the span for maximum

deflection calculation. The ANSYS model assumes 10,000 significant load cycles per day.

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Figure 3 Figure 4

Simplification Gusset Plate

6. Truss Deterioration Assumption: Many factors play into the deterioration of a Truss Bridge, most

notably Fatigue, Fatigue cracking at gusset plate connections, excessive truck loading and a lack of

redundancy in the mainframe of the truss bridge.

To simplify and summarise all these factors in ANSYS, the Modulus of Elasticity (E) will be reduced by,

modelling the reduction in Stiffness (E I).

Program Selection & Other ANSYS Assumptions

The truss bridge will be modelled using the (ANSYS 11.0) finite element analysis software. The type of

element used for this Analysis is the structural mass (LINK1 --> 2D spar) element for all the beams and

girders in the truss assembly. Metric units were used in Metres (m) for distances and spans and

Newtons (N) for loads.

• Constraints: The Truss Bridge assembly is fixed in all degrees of freedom at Keypoint #1,

bridge is pinned at Keypoint #9.

• The Control Modulus of Elasticity used is 200 GPa, and a Poisson's ratio of (0.29).

• The Modulus of Elasticity after 75 years of deterioration assumed as 0.02 GPa.

• Force due to truck loading: Simplified to point load of 356 kN.

• Total Dead Load (Self Weight) of the truss assembly is (818.24 kN) distributed equally at

Nodes (1 through 9) as (90.9 kN) Point Loads.

• ANSYS Analysis Type: Static Truss Analysis.

Problem Formulation

Before beginning the ANSYS analysis, hand calculations were used to solve for the internal reactions of

the beam-Girder configuration (By method of sections), and beams and girders are labeled according to

their reactions being in compression or tension. The loading used was strictly the dead loads of the

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Figure 5: ANSYS model showing mesh distribution and Nodal loading (Self Weight & Truck)

beams, and the results are used to stimulate where the weakest connection point in the truss

configuration may be present. Once these calculations were complete the Dead loads (Self weight) will

be simplified to the nodes numbered (1 - 9).

The ANSYS analysis of the Truss is done twice as follows:

1. The first part analysis, calculates the nodal deflection, reaction forces and stress for the Truss

configuration used. These results are to be used as a fixed control, to compare later with the

results due to 75 years of service.

2. The second part of the analysis, models the excessive loading after 75 years of service cycles,

nodal deflection, reaction forces and the stress for the truss configuration measured will be

compared to the control results.

Analysis

Part 1: Control Analysis:

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Figure 6: ANSYS model showing exaggerated deflection of the truss configuration

Part 2: Analysis After 75 year Cycle:

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Figure 7: ANSYS model showing Nodal Deflection Solution with the Red Colour indicating the max value

Figure 8: ANSYS model Axial Stress and the stress distribution along the Truss configuration

Figure 9: ANSYS model showing exaggerated deflection of the truss configuration

Results

Reaction Forces:

THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL COORDINATE SYSTEM

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Figure 10: ANSYS model showing Nodal Deflection Solution with the Red Colour indicating the max value

Figure 11: ANSYS model Axial Stress and the stress distribution along the Truss

CONTROL REACTIONSCONTROL REACTIONSCONTROL REACTIONS

NODE FX FY

1 2.33E-09 5.87E+05

9 5.87E+05

Total 2.33E-09 1.17E+06

REACTIONSREACTIONSREACTIONS

NODE FX FY

1 -6.46E-09 5.87E+05

9 5.87E+05

Total -6.46E-09 1.17E+06Table 3 Table 4

Deflection:

Axial Stress:

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THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN

THE GLOBAL COORDINATE SYSTEM

NODE UX UY UZ USUM

1 0.0000 0.0000 0.0000 0.0000

2 0.23856E-08-0.36154E-07 0.0000 0.36232E-07

3 0.67197E-08-0.66371E-07 0.0000 0.66711E-07

4 0.12565E-07-0.88218E-07 0.0000 0.89108E-07

5 0.19485E-07-0.10255E-06 0.0000 0.10439E-06

6 0.26405E-07-0.88218E-07 0.0000 0.92084E-07

7 0.32250E-07-0.66371E-07 0.0000 0.73792E-07

8 0.36585E-07-0.36154E-07 0.0000 0.51435E-07

9 0.38970E-07 0.0000 0.0000 0.38970E-07

10 0.69198E-08-0.30047E-07 0.0000 0.30833E-07

11 0.93055E-08-0.61383E-07 0.0000 0.62085E-07

12 0.13640E-07-0.84348E-07 0.0000 0.85444E-07

13 0.19485E-07-0.97053E-07 0.0000 0.98989E-07

14 0.25331E-07-0.84348E-07 0.0000 0.88070E-07

15 0.29665E-07-0.61383E-07 0.0000 0.68175E-07

16 0.32050E-07-0.30047E-07 0.0000 0.43932E-07

MAXIMUM ABSOLUTE VALUES

NODE 9 5 0 5

VALUE 0.38970E-07-0.10255E-06 0.0000 0.10439E-06

THE FOLLOWING DEGREE OF FREEDOM RESULTS ARE IN

THE GLOBAL COORDINATE SYSTEM

NODE UX UY UZ USUM

1 0.0000 0.0000 0.0000 0.0000

2 0.23856E-04-0.36154E-03 0.0000 0.36232E-03

3 0.67197E-04-0.66371E-03 0.0000 0.66711E-03

4 0.12565E-03-0.88218E-03 0.0000 0.89108E-03

5 0.19485E-03-0.10255E-02 0.0000 0.10439E-02

6 0.26405E-03-0.88218E-03 0.0000 0.92084E-03

7 0.32250E-03-0.66371E-03 0.0000 0.73792E-03

8 0.36585E-03-0.36154E-03 0.0000 0.51435E-03

9 0.38970E-03 0.0000 0.0000 0.38970E-03

10 0.69198E-04-0.30047E-03 0.0000 0.30833E-03

11 0.93055E-04-0.61383E-03 0.0000 0.62085E-03

12 0.13640E-03-0.84348E-03 0.0000 0.85444E-03

13 0.19485E-03-0.97053E-03 0.0000 0.98989E-03

14 0.25331E-03-0.84348E-03 0.0000 0.88070E-03

15 0.29665E-03-0.61383E-03 0.0000 0.68175E-03

16 0.32050E-03-0.30047E-03 0.0000 0.43932E-03

MAXIMUM ABSOLUTE VALUES

NODE 9 5 0 5

VALUE 0.38970E-03-0.10255E-02 0.0000 0.10439E-02

Control Deflection: Deflection:

ElementAxial Stress

ElementAxial Stress

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1595.4 173 234 277 277 234 173 95.4 -180 153 -147 125 -114 96.7 -8116 17 18 19 20 21 22 23 24 25 26 27 28 29138 -81 96.7 -114 125 -147 153 -180 -95 -173 -234 -234 -173 -95

Control Axial Element Stress:

ElementAxial Stress

ElementAxial Stress

1 2 3 4 5 6 7 8 9 10 11 12 13 14 1595.4 173 234 277 277 234 173 95.4 -180 153 -147 125 -114 96.7 -8116 17 18 19 20 21 22 23 24 25 26 27 28 29138 -81 96.7 -114 125 -147 153 -180 -95 -173 -234 -234 -173 -95

Axial Element Stress:

Table 5

Table 6

Discussion:

The results are most interesting, with a large reduction in the Modulus of Elasticity (Assumed with the

deterioration of the truss assembly), the FEA program ANSYS yielded relatively the exact same Axial

Stresses in both cases, a small variation in the reaction force at Node #1. The most notable difference,

that this project aims to highlight, is the significant change in deflection.

The deflection of the truss assembly is initially (-0.10255 x 10-6 m) and went up several orders of

magnitude to (-0.10255 x 10-2 m), at the middle of the span (Refer to Node #5). This large change in

magnitude would suggest a predication for a significant failure at multiple points for the truss bridge

assembly.

ConclusionThe ANSYS analysis for this Truss Bridge is very insightful, even with many factors being omitted in

the analysis. The results are very interesting in that the exaggerated change in (E) did not yield any

changes in the Axial Stress nor the Reaction forces of the Truss configuration, neither does this changes

the internal forces of the beams and girders. The change was most notable in the value of deflection,

which is an important value to study in bridge failures.

Results & Improvements to Model:

I am very satisfied with the results I have yielded with this analysis, and if I had more time, given more

time and properties, I could have incorporated many more properties into the analysis, such as the

geometry of the steel beams and girders used, the presence of the gusset plates at each connection

point, as well as the affect of the cross bracing truss members that contribute to the general stiffness of

the over all truss configuration. I would also incorporate the entire 3-Dimensional configuration of the

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truss bridge, along with properties for the concrete pavement and girders used to form the four-lane

road.

Finite Element Methods Discussion:

The Finite Element analysis software used for this project is ANSYS 11.0, and was run directly using the university’s server & HAMMER (interactive login cluster) on my personal computer at home.

Most of the assumptions used for this analysis were attained using the help of Dr. Edward Gannon (ejg3@psu.edu), a professor in the Civil Engineering Department, whose input was important in helping simply the Truss configuration for me and making it workable on ANSYS.

In reference to my results formulation on ANSYS, the truss configuration was meshed once only, since the important factor in my results, deflection, did not get affected my increasing the mesh size, nonetheless, as simple as the truss configuration I used, meshing any more would not have yielded any difference in results.

The text INPUT used to formulate my project is attached below in the Glossary section, the text file does not include however the different varying solutions I have sought for the results of my project.

The accurate results of an FEA model is very impressive and forms the basis of other softwares used

more specifically for Civil Engineering purposes such as SAP2000 and STAADpro.

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ELEMENT USED

TIME ELAPSED FOR

ANALYSISLICENSE USED

LINK 1 ~ 15 seconds ANSYS 11.0

AppendixHand Calculations:

The hand calculations performed for this projected included:

1. Self Weight of the 2-D truss assembly, using approximate AISC beam sizes.

2. The force reactions due to the self weight plus the weight of truck loading.

3. The internal reactions of the truss members using the method of sections.

4. AASHTO Bridge typical weight approximates for truss bridges of varying spans.

5. Axial Stress using (F/A)

List of Figures

1. Cover image: Walh Truss Bridge. [Online image] Available http://www.dcctrain.com/images/walh_corner_bridge.jpg, Dec 1, 2009.

2. Figure 1: Simple Span Truss Bridge. [Online image] Available http://www.con-span.com/DYOBTruss/, Dec 1, 2009

3. Figure 2: ANSYS model showing member and nodal assignment.

4. Figure 3: Gusset Plate simplification, drawn in Paint.

5. Figure 4: Gusset Plates. [Online image] Available http://images.publicradio.org/content/2007/08/09/20070809_gussetplate_2.jpg, Dec 1, 2009.

6. Figure 5: ANSYS model showing mesh distribution and Nodal loading (Self Weight & Truck)

7. Figure 6: ANSYS model showing exaggerated deflection of the truss configuration

8. Figure 7: ANSYS model showing Nodal Deflection Solution with the Red Colour indicating the max value

9. Figure 8: ANSYS model Axial Stress and the stress distribution along the Truss configuration

10. Figure 9: ANSYS model showing exaggerated deflection of the truss configuration

11. Figure 10: ANSYS model showing Nodal Deflection Solution with the Red Colour indicating the max value

12. Figure 11: ANSYS model Axial Stress and the stress distribution along the Truss configuration. (After 75 Years Cycle)

List of Tables

1. Table 1: Geometric Properties Table (summary)

2. Table 2: Nodal (Keypoint) assignment t the coordinate system.

3. Table 3: Table summarising ANSYS results for the Reaction forces in the X and Y directions (CONTROL)

4. Table 4: Table summarising ANSYS results for the Reaction forces in the X and Y directions

5. Table 5: Table summarising ANSYS results for the nodal deflection in the X and Y directions (CONTROL)

6. Table 6: Table summarising ANSYS results for the nodal deflection in the X and Y directions

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GlossaryANSYS Text Input as follows:

/PREP7 ! preprocessor phase! define keypoints

K,1, 0,0K,2, 5,0

K,3, 10,0K,4, 15,0

K,5, 20,0K,6, 25,0

K,7, 30,0K,8, 35,0

K,9, 40,0K,10, 35,8

K,11, 30,8K,12, 25,8

K,13, 20,8K,14, 15,8

K,15, 10,8K,16, 5,8

! define linesL,1,2

L,2,3L,3,4

L,4,5L,5,6

L,6,7L,7,8

L,8,9L,9,10

L,10,8L,8,11

L,11,7L,7,12

L,12,6L,6,13

L,13,5L,13,4

L,4,14L,14,3

L,3,15L,15,2

L,2,16L,16,1

L,16,15L,15,14

L,14,13L,13,12

L,12,11L,11,10

!*ET,1,LINK1

!*R,1,3250, ,

!*!*

MPTEMP,,,,,,,,MPTEMP,1,0

MPDATA,EX,1,,200e9MPDATA,PRXY,1,,0.29

! /REPLOT,RESIZE! /REPLOT,RESIZE

! /REPLOT,RESIZE! /REPLOT

! LPLOT! /PNUM,KP,1

! /PNUM,LINE,1! /PNUM,AREA,0

! /PNUM,VOLU,0! /PNUM,NODE,0

! /PNUM,TABN,0! /PNUM,SVAL,0

! /NUMBER,0!*

! /PNUM,ELEM,0! /REPLOT

!*!*

LESIZE,ALL, , ,1, ,1, , ,1,FLST,2,29,4,ORDE,2

FITEM,2,1FITEM,2,-29

LMESH,P51X! /PNUM,KP,1

! /PNUM,LINE,0! /PNUM,AREA,0

! /PNUM,VOLU,0! /PNUM,NODE,1

! /PNUM,TABN,0! /PNUM,SVAL,0

! /NUMBER,0!*

! /PNUM,ELEM,0! /REPLOT

!*ANTYPE,0

FLST,2,1,3,ORDE,1FITEM,2,1

!*/GO

DK,P51X, , , ,0,ALL, , , , , ,FLST,2,1,3,ORDE,1

FITEM,2,9!*

/GODK,P51X, , , ,0,UY, , , , , ,

FLST,2,1,3,ORDE,1FITEM,2,5

FLST,2,1,3,ORDE,1FITEM,2,5

FLST,2,1,3,ORDE,1FITEM,2,5

!*/GO

FK,1,FY,-90.916e3FK,2,FY, -90.916e3

FK,3,FY, -90.916e3FK,4,FY, -90.916e3

FK,5,FY, -446.916e3FK,6,FY, -90.916e3

FK,7,FY,- 90.916e3FK,8,FY,- 90.916e3

FK,9,FY,- 90.916e3FINISH

/SOL!*

ANTYPE,0! /STATUS,SOLU

SOLVEFINISH

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Bibliography & Programs Used1. ANSYS-386/ED Reference Manual

2. American Association of State Highway and Transportation Officials. AASHTO LRFD Bridge Design Specifications, Washington (District of Columbia)

3. Truss Bridges: http://en.wikipedia.org/wiki/Truss_bridge

4. Logan, Daryl L. A First Course in the Finite Element Method. Detroit: Cengage-Engineering, 2006. Print.

5. Steel Construction Manual, 13th Edition (Book). New York: American Institute of Steel Construction, 2006. Print.

6. Geschwindner, Louis F. Unified Design of Steel Structures. New York: Wiley, 2007. Print.

Program used:

1. ANSYS Version 11.0 Workbench.

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